Hydraulic fracture design optimization requires a vast number of simulation runs with various input combinations, something that is infeasible to fulfill manually as given the extended parameter space. In this study, we demonstrate a computationally efficient optimization process based on our simplified 3d displacement discontinuity method (S3D-DDM) hydraulic fracture model. We employ both pattern search and genetic algorithms to perform multi-variate optimization of hydraulic fracture effective contact area (ECA) in single and multi-cluster stage examples. For a fixed stage length, results reproduce the oft-cited numerical result that non-uniform cluster spacing leads to more uniform fracture area development and a larger ECA. With the presence of natural fractures, the optimization module locates the optimal cluster positions considering the interaction between both hydraulic-hydraulic and natural-hydraulic fractures. And the natural-hydraulic fracture interaction becomes the dominant factor of ECA expansion. Overall results show that both pattern search and genetic algorithms perform well and agree on the optimization strategy.
Hydraulic fracture modeling continues to evolve in sophistication since the hydraulic fracturing was made commercially viable. With the aid of various advanced numerical methods, modern hydraulic fracture models for horizontal wells simulate multiple hydraulic fracture propagation and the mechanical interactions between them (Wu and Olson, 2015; Ouchi et al., 2015; Kumar and Ghassemi, 2015; Lee at al., 2018). With the enrichment of the model functionality, it becomes infeasible to locate the optimal design by manual trial and adjustment, considering modern hydraulic fracture models have dozens of input parameters (Wang and Chen, 2013). In this circumstance, the term "optimization" in the studies of hydraulic fracturing often refers to improving the hydraulic fracturing efficacy through discrete manual adjustments of case input (Jamiolahmady et al., 2009; Saldungaray and Palisch, 2012), instead of granting the hydraulic fracture model an ability to search for the optimal input parameters on its own.
For an actual auto-optimization of the hydraulic fracturing design, a hydraulic fracture model needs to be bonded with optimization algorithms that can locate the optimal solution from a prescribed objective function. Ma et al. (2013) applied finite difference method, discrete simultaneous perturbation stochastic algorithm, and genetic algorithm (GA) to optimize the net present value of the well completion design by varying the positions of fixed-length planar hydraulic fractures. This study did not consider the dynamic propagation process of hydraulic fractures. Lee et al. (2018) used a phase-field hydraulic fracture model, in conjunction with GA, to optimize the total hydraulic fracture area from three-cluster cases by adjusting the cluster spacings. Case designs in this study are simple and small in scale – cluster spacings vary between 1.0 m to 1.5 m, and the hydraulic fractures are in 2D. Cheng and Bunger (2019) designed a reduced order model that simulates planar radial hydraulic fractures. Relying on the high efficiency of the model, they used exhaustive attack optimization that runs thousands of random input combinations instead of any optimization algorithm. Their study found that both limited entry and non-uniform fracture spacings facilitate the uniformity in hydraulic fracture growth. Yi et al. (2020) incorporated a pseudo-3D planar hydraulic fracture model with GA to optimize the fluid and proppant distribution and fracture contact area. They found that uniform treatment distribution improves the reservoir contact, and the uniformity of the treatment distribution is mostly affected by the perforation design. No matter which approaches to take, optimization is completed through repetitive evaluations of the hydraulic fracture model, which dramatically raises the computation intensity. Therefore, all the past studies mentioned above more or less sacrificed the fidelity of the physical model by limiting fracture geometry to 2D, planar, or radial. Moreover, they did not include naturally fractured reservoirs in their scopes, but the existence of natural fractures indeed alters hydraulic fracture geometry through the natural-hydraulic fracture interaction (Dahi Taleghani and Olson, 2013).